Packing Posets in the Boolean Lattice

الأصل · EN

We are interested in maximizing the number of pairwise unrelated copies of a poset P in the family of all subsets of [n]. We prove that for any P the maximum number of unrelated copies of P is asymptotic to a constant times the largest binomial coefficient. Moreover, the constant has the form 1/c(P), where c(P) is the size of the smallest convex closure over all embeddings of P into the Boolean lattice.